1. (a) In matrix notation the system can be written
as AX=B
where
[]
1116
1125
| and
3118
2237
x
ABXy
z
⎡⎤
⎡⎤
⎢⎥
−
⎢⎥
⎢⎥
==
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
−
⎣⎦
Applying R
2
−R
1
, R
3
− 3R
1
, R
4
− 2R
1
on [A | B]
we have
[]
32
42
1
2
2
1
43
3
1
3
3
1116
0211
|
02210
0415
1116
0211
2
0039
0013
1116
11
01
22
0013
0000
AB
RR
RR
R
RR
R
⎡⎤
⎢⎥
−−
⎢⎥
⎢⎥
−−−
⎢⎥
−−
⎣⎦
⎡⎤
−
⎢⎥
−−
⎢⎥
−
⎢⎥
−−
⎢⎥
−−
⎣⎦
⎡⎤
−
⎢⎥
⎢⎥
−
−
⎢⎥
−
⎢⎥
⎢⎥
⎢⎥
⎣⎦
∼
P(A) =P(A, B) = 3 = no. of unkno
wns. Hence
the system is consistent. It has a unique solu-
tion. By back substitution we hav
e z = 3, y = 2,
x = 1.
(b) In matrix notation line system can be writ-
ten as AX=B where
[]
14714
|38213 and
78265
x
ABXy
z
−
⎡⎤⎡⎤
⎢⎥⎢⎥
=−
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